PARACONSISTENT NEGATION AND CLASSICAL NEGATION IN COMPUTATION TREE LOGIC

Norihiro Kamide, Ken Kaneiwa

Abstract

A paraconsistent computation tree logic, PCTL, is obtained by adding paraconsistent negation to the standard computation tree logic CTL. PCTL can be used to appropriately formalize inconsistency-tolerant temporal reasoning. A theorem for embedding PCTL into CTL is proved. The validity, satisfiability, and model-checking problems of PCTL are shown to be decidable. The embedding and decidability results indicate that we can reuse the existing CTL-based algorithms for validity, satisfiability and model-checking. An illustrative example of medical reasoning involving the use of PCTL is presented.

References

  1. Almukdad, A. and Nelson, D. (1984). Constructible falsity and inexact predicates. Journal of Symbolic Logic, 49:231-233.
  2. Beziau, J.-Y. (1999). The future of paraconsistent logic. Logical Studies, 2:Online.
  3. Chen, D. and Wu, J. (2006). Reasoning about inconsistent concurrent systems: A non-classical temporal logic. In Lecture Notes in Computer Science, volume 3831, pages 207-217.
  4. Clarke, E. and Emerson, E. (1981). Design and synthesis of synchronization skeletons using branching time temporal logic. In Lecture Notes in Computer Science, volume 131, pages 52-71.
  5. Clarke, E., Grumberg, O., and Peled, D. (1999). Model checking. The MIT Press.
  6. da Costa, N., Beziau, J., and Bueno, O. (1995). Aspects of paraconsistent logic. Bulletin of the IGPL, 3 (4):597- 614.
  7. Easterbrook, S. and Chechik, M. (2001). A framework for multi-valued reasoning over inconsistent viewpoints. In Proceedings of the 23rd International Conference on Software Engineering, pages 411-420.
  8. Gurevich, Y. (1977). Intuitionistic logic with strong negation. Studia Logica, 36:49-59.
  9. Murata, T., Subrahmanian, V., and Wakayama, T. (1991). A petri net model for reasoning in the presence of inconsistency. IEEE Transactions on Knowledge and Data Engineering, 3 (3):281-292.
  10. Nelson, D. (1949). Constructible falsity. Journal of Symbolic Logic, 14:16-26.
  11. Odintsov, S. and Wansing, H. (2003). Inconsistencytolerant description logic: Motivation and basic systems. In Trends in Logic: 50 Years of Studia Logica, pages 301-335.
  12. Priest, G. and Routley, R. (1982). Introduction: paraconsistent logics. Studia Logica, 43:3-16.
  13. Rautenberg, W. (1979). Klassische und nicht-klassische Aussagenlogik. Vieweg, Braunschweig.
  14. Vorob'ev, N. (1952). A constructive propositional calculus with strong negation (in Russian). Doklady Akademii Nauk SSR, 85:465-468.
  15. Wagner, G. (1991). Logic programming with strong negation and inexact predicates. Journal of Logic and Computation, 1 (6):835-859.
  16. Wansing, H. (1993). The logic of information structures. In Lecture Notes in Computer Science, volume 681, pages 1-163.
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Paper Citation


in Harvard Style

Kamide N. and Kaneiwa K. (2010). PARACONSISTENT NEGATION AND CLASSICAL NEGATION IN COMPUTATION TREE LOGIC . In Proceedings of the 2nd International Conference on Agents and Artificial Intelligence - Volume 1: ICAART, ISBN 978-989-674-021-4, pages 464-469. DOI: 10.5220/0002699504640469


in Bibtex Style

@conference{icaart10,
author={Norihiro Kamide and Ken Kaneiwa},
title={PARACONSISTENT NEGATION AND CLASSICAL NEGATION IN COMPUTATION TREE LOGIC},
booktitle={Proceedings of the 2nd International Conference on Agents and Artificial Intelligence - Volume 1: ICAART,},
year={2010},
pages={464-469},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0002699504640469},
isbn={978-989-674-021-4},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 2nd International Conference on Agents and Artificial Intelligence - Volume 1: ICAART,
TI - PARACONSISTENT NEGATION AND CLASSICAL NEGATION IN COMPUTATION TREE LOGIC
SN - 978-989-674-021-4
AU - Kamide N.
AU - Kaneiwa K.
PY - 2010
SP - 464
EP - 469
DO - 10.5220/0002699504640469